Inconductingalargenumberofsignificancetests,the false discoveryrate (FDR) isthe expectedproportionoftherejectednullhypothesesthatareerroneouslyrejected.Asimple algorithm canensureFDR when appliedwith t independenttestsandisespeciallyuseful when asmallproportionofthenullhypothesesareexpectedtobefalse.Let P(1) P(2) P(t) denote theordered

Inconductingalargenumberofsignificancetests,the false discoveryrate (FDR) isthe expectedproportionoftherejectednullhypothesesthatareerroneouslyrejected.Asimple algorithm canensureFDR ≤ α when appliedwith t independenttestsandisespeciallyuseful when asmallproportionofthenullhypothesesareexpectedtobefalse.Let P(1) ≤ P(2) ≤ ⋯ ≤

P(t) denote theordered P-values.Themethodrejectshypotheses(1),…,(j∗), where j∗ is the maximum j for which P(j) ≤ jα~t.

(a) ExplainwhytheFDRandBonferronimakethesamedecisionforthemostsignificant test, butotherwisetheFDRmethodrejectsinatleastasmanycasesastheBonferroni method.

(b) Thestatisticians(YoavBenjaminiandYosefHochberg)whointroducedthismethodin 1995 illustratedtheFDRforastudyaboutmyocardialinfarction.Forthe15hypotheses tested inthestudy,theordered P-values(P(1),P(2), ...,P(15)) were 0.0001, 0.0004,0.0019,0.0095,0.020,0.028,0.030, 0.034, 0.046,0.32,0.43,0.57,0.65,0.76,1.00.

With α = 0.05, indicatewhichhypothesesarerejectedwiththeFDRmethodandwith the Bonferronimethod.